Tony Lawson claims that deductivism is synonymous with taxonomy.
This is not a misinterpretation of his views - his writing literally bristles with statements to this effect and even when referring obliquely to taxonomy, Lawson does not neglect to put deductivist in parenthesis to remind us that it is supposedly a synonym; e.g. lambasting “the overly taxonomic (deductivist) orientation to method (p. 972)” or yearning for the “demise of all overly taxonomic (including deductivist) approaches (p. 973).”
I disagree. I do not see even the slightest similarity between deductive logic and taxonomy. If there is anybody at Research Gate who sees any similarity, I would like to know what it is.
https://www.researchgate.net/publication/280948689_Critique_of_Tony_Lawson_on_Neoclassical_Economics
Research Critique of Tony Lawson on Neoclassical Economics
Dear Victor,
I disagree. There just might be a very slight connection between taxonomy and deductive logic. Deductive logic could be recognised as the study of valid [and meaningful] rules and rule-based reasonings. It mainly focuses on rules, searches through the relations between rules and searches through the various branches [and sub-branches] of rules in order to find the most appropriate rules (or the symbols that the rules have been defined on them). So, I may conclude that deductive logic searches through the taxonomy of rules.
Victor:
Your critic to Lawson is sound and strongly based upon logical knowledge. Sometimes the light knowledge of logic drive us to misunderstandigs. Taxonomy certainly is always vinculated to a given subject or content. Logic is not vinculated to any content. Taxonomy uses logical rules in the same way as Mathematics, Engineering, Physics, Chemistry, Robotics, Economics and Social Sciences in general, for Logic is an universal tool, Taxonomy is always a local or vinculated tool that "speaks" about the world, Logic does not. Taxonomy "populates" the world with its categories or its newly individuals, Logic does not. A revision of the Ludwig Wittgenstein's "Tractatus logico-philosophicus" will be necessary, specially the paragraphs 6.125 - 6.1262.
Farshad:
Logical experience taught us that trying to make a taxonomy of logical rules is an exercise only possibly in the first steps of deduction, within finitarian focusing with very few logical variables (ie
Dear Gabriel,
I certainly agree the obvious fact that logic searches through logical symbols, operators, rules, hypothesis, etc. But it is not a counter-fact for the fact that deductive logic searches (may search) through the taxonomy of rules. [Ofcourse,] logic does not definitely work with taxonomies. As I mentioned, I only brought a very slight connection between them. For instance, this is what we can obviously see in Gentzen Calculus. Or as another instance, relying on Rule-Expression Reasoning, we may consider that the rule R is valid in the case of predicate P1. Therefore R manifests itself in P1 ∧ P2, ¬ (P1 ∧ P2), P3 ∨ (P1 ∧ P2) and all huger (more specific and more complex) sentences over P1 that any one (sentence) can be identified as the parent of one other (sentence). P1 is the parent of P1 ∧ P2 and P1 ∧ P2 is the parent of ¬ (P1 ∧ P2), ... .
Dear Farshad,
The parental relationship between logical expressions is arbitrarily proposed upon a particular construction or a given logical operation. There are so many parental logical relationship as we can immagine, could it be at syntactical or semantical levels.
Taxonomies, classifications, orders, relationships, all are human decisions, constructs or better, impositions.
Let's take as an example the Borge's classification of animals:
those that belong to the Emperor,
embalmed ones,
those that are trained,
suckling pigs,
mermaids,
fabulous ones,
stray dogs,
those included in the present classification,
those that tremble as if they were mad,
innumerable ones,
those drawn with a very fine camelhair brush,
others,
those that have just broken a flower vase,
those that from a long way off look like flies
The same thing happens within the logical expressions, for example, let's say that we may decide to make a taxonomy based on those expressions which DNF has an only one disjunct, so all the xor-like operators at n-variables cases will enter within this class. In this sense your position is sound at rule-expression reasoning, but what happens when one cannot immagine, propose, nor impose any construction as a basis of a rule-expression reasoning search strategy. Logic has operative methods to go on such cases without previous classification or taxonomical information, for the milestone concept to efficiently guide a search, is that of logical structure and not that of similarity. In this sense I agree, it is not a counter-fact that taxonomic or resemblance-reasoning can take place at logical procedures, as it is neither a counter-fact that the brut force technique can be used to solve a logical problem, but consider that it can take millions of years to find out an only one resemblance between logical expressions to solve a logical problem within a high cardinality logical universe. Nowadays the work of the hungarian chemist Stephen Anthony Kiss -collaborator of Garrett Birkhoff-, passed by in 1948, is being rediscovered (https://projecteuclid.org/euclid.bams/1183512103).
Dear Colin.
I really appreciate your answer for it illustrates the nowadays level of logical involvement within computer and cognitive areas. I'll write you more on this topic latter, but now I only wish to make an annotation for your comment on the Dr Stephen A Kiss (effectively he is listed on patents in the 30's) "So what?"
It happens that this focusing on ternary operations is precisely proposed at the 30's decade, please feel free to give me a similar exemple of the nowadays called
" cascades of and-or gates" proposed at these or later decades.
Gabriel
the scopes of taxonomy and logic are fundamentally different. When taxonomy says "look into all details in order to understand how things developed", logic says "forget unessential details and find the most abstract and general principle". However, they are happily interconnected in many ways - and this is good so, because any intellectual activity must be somehow connected to logic, in order to exist. Taxonomy needs a lot of logical thinking in its proofs and argumentation. There are situations which are really difficult to decide, specially in biology, when you really must ask yourself which function could have been more important for this evolution and ao on. Logic needs a very clear taxonomy of its own categories by the definition of every new setting. This happens naturally more at the level of its syntax (related also lexically with Taxa, taxon, taxonomy - and do not forget that syntax was at the beginning a taxonomy of languages.) And only a robust and clear syntax assures a well working semantics.
But, of course, one should not make logic or even deduction as a particular case of taxonomy. No way.
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